Can you paint textures in Blender 2.8x with values > 1? (I.e. HDR)
I'd like to paint them as they should be.


Not really sure what that means. Art is trickery. The only rule is, "if it looks good, it is good".

That being said, one way to do what you want would be to texture paint on an image, assign that as the color input to an Emission node, and crank the Emission node strength up to 200 or whatever.

If you feel fancy, you could add multiple textures to a single object with a Mix Shader.